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The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
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Constant flux relation for diffusion-limited cluster-cluster aggregation.

Colm Connaughton1, R Rajesh, Oleg Zaboronski

  • 1Centre for Complexity Science, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom. connaughtonc@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2008
PubMed
Summary
This summary is machine-generated.

A constant flux relation (CFR) in nonequilibrium systems dictates scaling for conserved quantities. This study derives and verifies the CFR for cluster-cluster aggregation, revealing its unique, dimension-independent nature in diffusion-limited aggregation.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Non-equilibrium Dynamics

Background:

  • Non-equilibrium systems exhibit unique scaling behaviors governed by conserved quantities.
  • Constant Flux Relations (CFR) link conserved fluxes to correlation function scaling, independent of mean-field applicability.
  • Cluster-cluster aggregation models with monomer sources in diffusion-limited regimes present complex steady-state dynamics.

Purpose of the Study:

  • To derive the CFR for binary aggregation with a general scale-invariant kernel in the diffusion-limited regime.
  • To investigate the 'locality criterion' essential for realizing CFR scaling.
  • To examine the breakdown of CFR scaling due to locality violations or finite size effects.

Main Methods:

  • Derivation of the CFR for the flux-carrying correlation function in binary aggregation.
  • Analytical investigation of the 'locality criterion' using the mean-field Smoluchowski equation.
  • Perturbative analysis of dimensionality effects on locality.
  • Numerical simulations in one dimension to verify locality.

Main Results:

  • A unique CFR exponent was derived for binary aggregation, independent of system dimension and transport mechanism details.
  • The 'locality criterion' was shown to be satisfied at the mean-field level and holds for dimensions above the critical dimension (d_c=2).
  • Numerical simulations confirmed locality in one-dimensional systems.
  • CFR scaling breakdown was illustrated under locality violation and finite size effects.

Conclusions:

  • The derived CFR exponent offers a universal characteristic for diffusion-limited binary aggregation.
  • The 'locality criterion' is crucial for the validity of CFR scaling, particularly in lower dimensions and fluctuation-dominated regimes.
  • Understanding locality and finite size effects is key to predicting scaling behavior in complex aggregation processes.